Optical scanning device and imaging apparatus implementing the same

ABSTRACT

An optical scanning device, including a resin lens having a power that is an inverse power of scanning lens placed before a deflector. A bundle of rays emitted from a plurality of light sources is coupled into a desired state by coupling lens, after which the bundle of rays is incident on the resin lens. The surface of incidence of the resin lens has a spherical surface with a negative power, and the exit surface of this resin lens has a cylindircal surface with a negative power only in the sub scanning direction. The bundle of rays passes through the resin lens and enters a glass toroidal lens. A light deflector deflects the bundle of rays from the toroidal lens. The deflected bundle of rays is incident on a third optical system that condenses the deflected bundle of rays onto a surface to be scanned.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to an optical scanning deviceand an imaging apparatus implementing this optical scanning device, andparticularly to a multi-beam optical scanning device that simultaneouslyscans a surface to be scanned such as a photoconductor using a pluralityof light beams so as to significantly increase recording speed, thismulti-beam optical scanning device being suitable for use in a writesystem of a recording device such as a digital copier, a laser printer,or a laser facsimile.

2. Description of the Related Art

One known method of increasing the recording speed of an opticalscanning device implemented in a write system of a recording device suchas a laser printer or a laser facsimile is a method of increasing therotation speed of a polygon mirror, which functions as a deflector.However, in this method, factors such as the durability of the motor,the noise, the oscillation, and the modulation speed of thesemiconductor laser impose limitations on attempts at increasing therecording speed. Thus, a multi-beam optical scanning device thatincreases recording speed by simultaneously scanning a plurality oflight beams to record a plurality of scanning lines at once is beingproposed.

Also, technology for forming the scanning lens with resin is beingdeveloped in order to realize cost reduction and formation of aparticular lens surface.

However, it is known that the change in the curvature radius or therefractive index due to a change in environmental temperature and thelike is greater in a resin lens than in a lens made of glass. Thereby,in a multi-beam scanning optical system using the resin lens, thescanning line spacing for the plurality of scanning lines in thesub-scanning direction (referred to as ‘beam pitch’ hereinafter) isvaried, causing image degradation such as unevenness in image density.

FIG. 1 is a diagram showing the light path of principal rays in the subscanning direction in an optical scanning device according to therelated art. In this optical scanning device, a glass coupling lens 102and a glass cylindrical lens 104 are used as a first optical system anda second optical system, respectively. Also, a two-channel LDA (laserdiode array) 101 is shown as a light source. Further, resin lenses 161and 162 (scanning lens) make up a third optical system.

In the following, the change in the beam pitch in response to a changein temperature will be described.

First, a beam pitch P′ on an image surface can be expressed by thefollowing formula:P′=P ₀ ×Fcyl/Fcol×βwherein P₀ denotes the beam spacing in the sub scanning direction at thelight source, Fcol denotes the focal length of the first optical system,Fcyl denotes the focal length of the second optical system, and βdenotes the lateral magnification in the sub scanning direction of thethird optical system.

Since the change in P₀, Fcol, and Fcyl due to temperature change istrivial and can be disregarded, the change in the beam pitch can bedescribed in conjunction with the change in the lateral magnification inthe sub scanning direction of the third optical system made up of theresin lenses 161 and 162. That is, the change in the lateralmagnification in the sub scanning direction of the third optical systemdue to temperature change is directly reflected in the change in thebeam pitch. The light path indicated by dotted lines in FIG. 1 is thelight path when the temperature is increased. That is, the beam pitchincreases as a result of an increase in the temperature.

Also, in the optical scanning device, a bundle of rays emitted from aplurality of emission points is normally converted into a bundle ofparallel rays via the coupling lens 102 (first optical system), and isformed into a line image that extends along the main scanning directionby the cylindrical lens 104 (second optical system), this beingperformed in the vicinity of a polygon mirror 105. The polygon mirror105 deflects each bundle of rays that is emitted via the cylindricallens 104, and scans this at a substantially isometric speed (constantlinear velocity). The scanning lenses 161 and 162 of the third opticalsystem form an image on a surface to be scanned 107 by condensing eachbundle of rays deflected and scanned by the polygon mirror 105. However,in order to enhance flexibility in optical design, the bundle of raysemitted from a plurality of emission points is preferably converted intoa bundle of diverging rays or convergent rays at the coupling opticalsystem in accordance with the characteristics of the optical systemsfollowing the coupling optical system.

In the multi-beam optical scanning device, given that the emission pointpositions (emission point spacing) change by P1 under the influence oftemperature change or a difference in the mounting of the light sourcedevice, the beam spacing at the surface to be scanned 107 changes (isdegraded) by P, which can be expressed by the formula below:

P=P1×m (m: magnification in the sub scanning direction between the lightsource and the surface to be scanned)

Thus, to obtain stable beam spacing in the sub scanning direction at thesurface to be scanned 107, the magnification in the sub scanningdirection between the light source and the surface to be scanned 107 ispreferably low.

In turn, to lower the magnification in the multi-beam optical scanningdevice, the bundle of rays emitted from a plurality of emission pointsis preferably converted into a bundle of diverging rays at the couplingoptical system.

When the bundle of rays emitted from a plurality of emission points isconverted into a bundle of diverging rays via the coupling opticalsystem, the principal rays of the bundle heading toward the same imageheight will be parallel (the field angles are equal). Herein, if thescanning lens has functions of imaging parallel rays, the surface to bescanned 107 will be adjusted to a focus point of the bundle of rays(imaging point of the diverging rays). However, the focus point of thebundle of rays and the intersecting point of the principal rays (theintersecting position of the parallel rays) do not meet at the samepoint. Thus, when the surface to be scanned 107 is adjusted to the focuspoint, a displacement of dots in the main scanning direction occurs.Also, since the image height at the start of writing and the imageheight at the end of writing form different angles at the deflectionsurface of the deflector (e.g. reflection angle of the polygon mirror),the write width (scanning width) of each beam is different and deviationbetween the beams is created. If the emission points are not spaced outin the main scanning direction (e.g. the emission points of thesemiconductor laser array are arranged to be aligned in the sub scanningdirection), the displacement of dots in the main scanning direction andthe difference in the write width between each of the beams can beprevented. However, the above arrangement is difficult to realize sinceerrors during the mounting of the devices and the like cannot becompletely eliminated.

Also, in a case where the scanning lens (third optical system) has afunction of imaging diverging rays, each bundle of rays is focused atthe surface to be scanned 107. However, if the principal rays of eachbeam emitted from the different emission points are parallel, the raysintersect before reaching the surface to be scanned 107 (towards thedeflector) and thus the image heights will differ at the surface to bescanned 107. Also, since the image height at the start of writing andthe image height at the end of writing form different angles at thedeflection surface of the deflector (e.g. reflection angle of thepolygon mirror), the write width (scanning width) of each beam isdifferent and deviation between the beams is created. Further, thedifference in image heights will still exist even when the image heightat the start of the writing is adjusted according to the image height atthe end of writing.

As described above, when the bundle of rays that has passed through thecoupling optical system is converted into diverging rays, degradation ofthe image such as unevenness in density or distortion of the verticallines may occur due to the displacement of dots in the main scanningdirection or the difference in the write width (scanning width) of eachbeam.

In recent years, technologies for increasing the density of the imagereproduced by the digital copier or the laser printer have beendeveloped, and with this continuing development, the miniaturization ofthe beam spot diameter on the photoconductor is in demand. However, asmentioned above, a resin lens induces a greater change in the curvatureradius or the refractive index due to a change in environmentaltemperature and the like compared to a glass lens. When a fieldcurvature is generated as a result of the above change in the curvatureradius or the refractive index, the beam spot written on thephotoconductor will be enlarged, leading to image degradation.

In Japanese Patent Laid-Open Publication No. 8-292388, an opticalscanning device developed in response to the above described problems isdisclosed. Since the change in the field curvature due to temperaturechange at the positive lens and the change in the field curvature due totemperature change at the negative lens are inverses (negatives) of eachother, the optical scanning device according to this prior art inventionis arranged to compensate for the change in field curvature byimplementing a scanning resin lens and another resin lens having theinverse power of the scanning lens on the light path between the lightsource and the light deflector so that the change in field curvaturecaused by temperature change in the scanning lens is canceled out.However, the resin lenses implemented between the light source and thelight deflector have no power in the main scanning direction and thushave no compensation capabilities for the change in field curvature inthe main scanning direction caused by the temperature change of theresin scanning lens. Therefore, the enlargement of the beam spotdiameter in the main scanning direction cannot be prevented in thisprior art invention.

Also, in order to improve the shape of the beam spot in the sub scanningdirection, compensation for wave aberration from the standpoint of waveoptics needs to be considered as well as compensation for fieldcurvature from the geometric-optical standpoint. In an optical scanningdevice disclosed in Japanese Patent Laid-Open Publication No.8-292388,all resin lenses having a negative power are arranged to beplano-concave cylindrical lenses. However, as described in the preferredembodiments of this patent application, the curvature radii will bequite small at around 5 mm or 8 mm according to this prior artinvention. Thereby, a higher level of processing precision and/ormounting precision will be required. The problem with this prior artinvention is that the temperature compensating function is provided onlyon one surface of the lens.

Also, in a light beam scanning optical device disclosed in PatentGazette Publication No.2804647, the compensation for field curvature inthe main scanning direction is realized by a resin lens that has a poweropposite (negative) to the power of the scanning resin lens. However,for the sub scanning direction, the change in field curvature iscontrolled by restricting the mounting position of the scanning lens.With this arrangement, the flexibility in design will also berestricted. Further, this light beam scanning optical device compensatesfor the field curvature in the sub scanning direction by using acylindrical resin lens that has a negative power. However, thetemperature compensation function is only provided on one surface of thelens. (In the light beam scanning optical device claimed in claim 9 ofthe Patent Gazette Publication No.2804647, one side of the lens havingthe negative power has an axially symmetric aspherical surface and theother side has a cylindrical surface, thereby providing negative powersto both surfaces; however, the axially symmetric aspherical surface ismainly for compensating for the field curvature in the main scanningdirection and thus has weak power and the compensation for the fieldcurvature in the sub scanning direction is mainly realized by the othercylindrical surface, which has the stronger power.) Therefore, thecurvature radius of the cylindrical surface will be small, and a higherlevel of processing precision and mounting precision will be required.

Also, in a laser beam scanning optical device disclosed in JapanesePatent Laid-Open Publication No.10-20225 or a scanning optical devicedisclosed in Patent Gazette Publication No.2761723, the misplacement ofthe image formation position due to temperature change is compensatedfor by moving a collimator lens and the like towards the optical axisusing a mechanical structure so as to adjust the image formationposition mechanically. However, costs will be raised and the powerconsumption of the device will increase due to the extra parts requiredfor the mechanical structure and a detector that detects themisplacement of the image formation position.

As described above, in the resin lens, the change in the curvatureradius or the refractive index due to environmental temperature changeis greater compared to a glass lens, and therefore, a field curvature isgenerated in the optical system that implements the resin lens and thebeam spot diameter formed on the photoconductor is enlarged, resultingin image degradation. Various technologies for countering the aboveproblem have been proposed in the prior art inventions; however, therehave been no disclosures of an optical scanner device implementing aresin lens as the scanning lens that is capable of preventing theenlargement of a beam spot without requiring greater processingprecision or mounting precision, and also without increasing costs byimplementing additional mechanical parts or detection parts.

SUMMARY OF THE INVENTION

The present invention has been developed in response to the abovedescribed problems of the related art, and its object is to provide anoptical scanning device that implements a resin lens having a power thatis an inverse power of the scanning lens in an optical system placedbefore a deflector so that a change in the beam pitch due toenvironmental temperature change can be controlled even when a resinlens is used as a scanning lens.

Also, it is an object of the present invention to realize a reduction ofcosts and power consumption in an optical scanning device that convertsa bundle of rays passing through a coupling optical system intodiverging rays and lowers magnification in a sub scanning directioncompared to the related art in which a displacement of dots in the mainscanning direction or a difference in the write width (scanning width)of each beam are prevented, a misplacement of an image formationposition is compensated for, and the image formation position isadjusted mechanically.

More specifically, a multi-beam optical scanning device according to thepresent invention includes:

a light source having a plurality of emission points that emit a bundleof rays;

a first optical system that couples the bundle of rays emitted from thelight source;

a second optical system that condenses the bundle of rays emitted fromthe first optical system into a substantially linear state extendingalong a main scanning direction;

a light deflector that has a deflection surface arranged close to wherethe bundle of rays is condensed, wherein the bundle of rays is deflectedby this deflection surface;

a third optical system that condenses the deflected bundle of rays ontoa surface to be scanned as a plurality of light spots; wherein

the third optical system has at least one resin imaging element;

the second optical system has at least one resin imaging element and atleast one glass imaging element; and

the power of each surface of the resin imaging element of the secondoptical system is arranged so that a change in beam pitch in a subscanning direction caused by a temperature change in at least one of thefirst optical system and the third optical system satisfies a condition:ΔP′<0.5/DPI (mm/° C.)wherein ΔP′ denotes a measure of change in the sub scanning beam pitchon an image surface for every 1° C. temperature change (mm/° C.), andDPI denotes a write density (dots/inch).

Alternatively, a multi-beam optical scanning device according to thepresent invention includes:

a light source having a plurality of emission points that emit a bundleof rays;

a first optical system that couples the bundle of rays emitted from thelight source into a bundle of diverging light rays;

a second optical system that condenses the bundle of rays emitted fromthe first optical system into a substantially linear state extendingalong the main scanning direction;

a light deflector that has a deflection surface arranged close to wherethe bundle of rays is condensed, wherein the bundle of rays is deflectedby this deflection surface;

an aperture stop arranged between the first optical system and the lightdeflector

a third optical system that condenses the deflected bundle of rays ontoa surface to be scanned as a plurality of light spots; wherein

the third optical system has at least one resin imaging element;

the second optical system has at least one resin imaging element and atleast one glass imaging element; and

the resin imaging element of the second optical system has a negativepower in the sub scanning direction and a surface configuration that isarranged to effectively compensate for a change in field curvaturecaused by a temperature change in at least one of a support member ofthe first optical system and the resin imaging element in the thirdoptical system.

Further, the resin imaging element of the second optical system of theabove optical scanning device may have a negative power in the mainscanning direction.

The second optical system as a whole may have a positive power in themain scanning direction.

The bundle of rays emitted from the second optical system may be abundle of substantially parallel rays in the main scanning direction.

Also, a plurality of emission points of the light source may be spacedout in the main scanning direction.

The aperture stop may be arranged between the first optical system andthe second optical system and may be arranged to satisfy a condition:L1<L2wherein L1 denotes a distance from an optical element of the firstoptical system that is closest to the light deflector to the aperturestop, and L2 denotes a distance from the aperture stop to an opticalelement of the second optical system closest to the light source.

Additionally, the resin imaging element of the second optical system mayhave at least two surfaces that have negative powers in the sub scanningdirection, the surfaces being configured to effectively compensate forthe change in field curvature caused by a temperature change in at leastone of a support member of the first optical system and the resinimaging element of the third optical system.

The second optical system may have at least two resin imaging elementsthat have negative powers in the sub scanning direction.

Further, the light source is preferably a laser diode array that has aplurality of emission points.

The imaging element of the second optical system that has the power inthe sub scanning direction is preferably positioned so as to allow abeam waist (minimum beam spot size) in the sub scanning direction to bepositioned substantially on the surface to be scanned.

Further, the imaging element of the second optical system may only havethe power in the sub scanning direction.

The imaging element of the second optical system that has the power inthe main scanning direction is preferably positioned so as to allow abeam waist in the main scanning direction to be positioned substantiallyon the surface to be scanned.

The above imaging element of the second optical system may only have thepower in the main scanning direction.

According to another aspect, the present invention is an imagingapparatus that implements the above described optical scanning device.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram showing the light path of principal raysin the sub scanning direction in an optical scanning device according tothe related art;

FIGS. 2A and 2B show an optical scanning device according to anembodiment of the present invention;

FIG. 3 is a schematic diagram showing the light path of principal raysin the sub scanning direction in the optical scanning device shown inFIGS. 2A and 2B;

FIG. 4 shows the relationship between image height and scanning lineposition in the optical scanning device of the present invention shownin FIG. 2B;

FIGS. 5A and 5B show an optical scanning device according to anotherembodiment of the present invention;

FIGS. 6A and 6B show an optical scanning device according to anembodiment of the present invention in which a power in the sub scanningdirection is dispersed onto three surfaces;

FIGS. 7A and 7B show examples of light ray bundles emitted from anemission point and passing through a first optical system and a secondoptical system in an optical scanning device that converts the rayspassing through the first optical system into parallel rays, and in anoptical scanning device that converts the rays passing through the firstoptical system into diverging rays;

FIGS. 8A and 8B show examples of light ray bundles between the emissionpoint and an aperture stop in an optical scanning device that convertsthe rays passing through the first optical system into parallel rays andin an optical scanning device that converts the rays passing through thefirst optical system into diverging rays;

FIG. 9 shows a cross-sectional view in the sub scanning direction of theoptical scanning device of the present invention wherein a distributionof the lens power and positions of the aperture stop are illustrated;and

FIG. 10 is a diagram of a laser printer illustrated as an example of animaging apparatus that implements the optical scanning device of thepresent invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

In the following, preferred embodiments of the present invention aredescribed with reference to the accompanying drawings.

FIGS. 2A and 2B are diagrams illustrating an optical scanning deviceaccording to a first embodiment of the present invention, wherein FIG.2A is a schematic diagram of the optical scanning device, and FIG. 2B isa side view (optical path) diagram of the same optical scanning device.In this embodiment, a plurality of light ray bundles emitted from alight source 1 are coupled into a desired state by means of a couplinglens 2 (first optical system). Herein, the rays are coupled intosubstantially parallel (or collimated) rays. Also, in this example, aLDA (laser diode array) having a plurality of emission points is used asthe light source 1. The light source 1 may also be a plurality of laserdiodes that emit multi-beam light synthesized by a prism.

By using a plurality of light sources as described above, the rotationspeed of a light deflector can be lowered, thereby extending the lifeand reducing the power consumption of the optical scanning device.

As for the coupling lens 2, a single aspherical lens may be used. Thewave aberration of the coupling lens on its own can be suitablycompensated for. The bundle of rays emitted from the coupling lens 2 isincident on a resin lens 10. A surface of incidence 10 a of the resinlens 10 has a spherical surface configuration that is provided with anegative power. Herein, the surface of incidence 10 a may be acylindrical surface that has a negative power only in the main scanningdirection.

Next, the bundle of rays emitted from the resin lens 10 are incident ona glass toroidal lens 12 via a resin lens 11 that has a negative poweronly in the sub scanning direction. Then the bundle of rays is arrangedinto substantially parallel rays with respect to the main scanningdirection and incident on a light deflector 5. With respect to the subscanning direction, the bundle of rays is condensed substantially into aline extending along the main scanning direction at a deflectionsurface. Herein, the glass toroidal lens 12 may have a spherical surfaceand a cylindrical surface, or it may be an assemblage of a cylindricallens and a spherical lens. Alternatively, the glass toroidal lens 12 mayhave two cylindrical surfaces with differing powers, or it may be madeof a glass cylindrical lens as long as the coupling state of the emittedlight from the coupling lens 2 is adjusted.

A third optical system 60 that includes resin lenses 61 and 62compensates for the field curvatures in the main scanning direction andthe sub scanning direction as well as optical characteristics such asfθ, and focuses the rays deflected by the light deflector 5 onto asurface to be scanned 7 while securing a desired sub scanning beam pitchon the surface to be scanned 7. Note that in the drawing, the partsindicated by numerals 10 a, 11 a, 12 a, 61 a, and 62 a correspond to theplanes of incidence of the resin lenses 10, 11, the glass toroidal lens12, and the resin lenses 61, 62, respectively. Also, the parts indicatedby numerals 10 b, 11 b, 12 b, 61 b, and 62 b correspond to exit surfacesof the resin lenses 10, 11, the glass toroidal lens 12, and the resinlenses 61, 62, respectively.

In the following, a change in the beam pitch due to a change intemperature will be described.

First, in FIG. 3 the beam pitch P′ on the image surface 7 can beexpressed by the following formula:P′=P ₀ ×Fcyl/Fcol×βwherein P₀ denotes the beam spacing in the sub scanning direction at thelight source 1, Fcol denotes the focal length of the first opticalsystem, Fcyl denotes the focal length of the second optical system 3that includes the resin lenses 10, 11, and the glass toroidal lens 12,and β denotes the lateral magnification in the sub scanning direction ofthe third optical system 60.

Since the change of P₀, Fcol, and Fcyl due to temperature change istrivial and can be disregarded, the change in the beam pitch can bedescribed in relation to the change in the lateral magnification of thethird optical system 60 made up of the resin lenses 61 and 62. That is,the change in the lateral magnification in the sub scanning direction ofthe third optical system 60 due to temperature change is directlyreflected in the change of the beam pitch.

FIG. 3 shows a light path of principal rays in the sub scanningdirection of the optical scanning apparatus shown in FIGS. 2A and 2B.

As described above, the resin lenses 10 and 11 of the second opticalsystem 3 have negative powers in the sub scanning direction. Thus, withan increase in the temperature, the focal distance Fcyl of the secondoptical system 3 becomes shorter and this causes the beam pitch to benarrower. In the third optical system 60, the focal distance increaseswith the increase in temperature, thereby causing the beam pitch toincrease. In this way, the change in the beam pitch is balanced out onthe whole.

It is preferable that the powers of the surfaces of the imaging elements(lenses) of the second optical system 3 be arranged so as to be capableof completely compensating for the change in the beam pitch in the subscanning direction caused by the temperature change in the first opticalsystem and/or the third optical system 60; however, setting the powersto satisfy the following formula will suffice for practical purposes.ΔP′<0.5/DPI (mm/° C.)Herein, ΔP′ denotes the change in the sub scanning beam pitch on theimage surface 7 for every 1° C. temperature change (mm/° C.), and DPIdenotes the write density (dots/inch).

When ΔP′ exceeds 0.5/DPI, image degradation such as unevenness indensity occurs. For example, if the write density is 1200 dpi (beampitch: 21.2 μm), the design temperature is 25° C., and the temperaturecan rise up to 45° C., the following value is obtained:0.5/1200×20=8.3 (μm)This will cause a problem in the image.

Note that in the embodiment using the LDA that has a plurality ofemission points as the light source, the change in the spacing of thelight source in the sub scanning direction P₀ due to temperature changecan be disregarded. However, if a plurality laser diodes are used aslight sources with the rays synthesized by a prism, the beam spacing inthe sub scanning direction, which corresponds to the interval of thelaser diodes, may possibly change in response to temperature changedepending on the mounting structure of the laser diodes. Therefore, itis preferable that the LDA having a plurality of emission points isused.

In the following, definition formulas of the surface configurations ofthe lenses in the present embodiment are shown.

Main Scanning Non-curvature Formula

The surface in the main scanning surface forms a non-curvatureconfiguration. Given that Rm denotes the paraxial curvature radius, Ydenotes the distance from the optical axis in the main scanningdirection, K denotes the conical constant, A1, A2, A3, A4, A5, A6, . . .denote the constants of the first and the higher order variables, and Xdenotes the depth in the optical axis direction, the following formulacan be obtained.X=(Y ² /Rm)/[1+√{square root over ( )}{1−(1+k) (Y/Rm)² }]+A1·Y+A2·Y ²+A3·Y ³ ·A4·Y ⁴ +A5·Y ⁵ +A6·Y ⁶+  (1)

Herein, when a value other than 0 is substituted for the coefficientsA1, A3, A5 . . . , which are the coefficients for Y that are powered byuneven numbers, an asymmetrical configuration is realized in the mainscanning direction. That is, when a value other than 0 is substitutedonly for the even numbered coefficients, symmetry is realized in themain scanning direction.

Sub Scanning Curvature Formula

The change in the sub scanning curvature in accordance with the mainscanning direction is expressed by a formula (2) indicated below:Cs(Y)=1/Rs(0)+B1·Y+B2·Y ² +B3·Y ³ +B4·Y ⁴ +B5·Y ⁵+  (2)

Sub Scanning Non-curvature Formula${X\left( {Y,Z} \right)} = {\frac{C_{m}Y^{2}}{1 + \sqrt{1 - {\left( {1 + K} \right)C_{m}^{2}Y^{2}}}} + {\sum\limits_{n = 1}^{p}{a_{n}Y^{n}}} + \frac{{C_{S}(Y)}Z^{2}}{1 + \sqrt{1 - \left( {1 + {{K_{Z}(Y)}{C_{S}^{2}(Y)}Z^{2}}} \right.}} + {\sum\limits_{j = 1}^{r}{\left( {\sum\limits_{h = 0}^{q}{d_{j,h}Y^{h}}} \right)Z^{j}}}}$Herein, the formula shown below:${f_{SAG}\left( {Y,Z} \right)} = {\sum\limits_{j = 1}^{r}{\left( {\sum\limits_{h = 0}^{q}{d_{j,h}Y^{h}}} \right)Z^{j}}}$can be broken down into the following: $\begin{matrix}{{f_{SAG}\left( {Y,Z} \right)} = {{\left( {{F0} + {{F1} \cdot Y} + {{F2} \cdot Y^{2}} + {{F3} \cdot Y^{3}} + {{F4} \cdot Y^{4}} + \ldots}\quad \right) \cdot Z} +}} \\{{\left( {{G0} + {{G1} \cdot Y} + {{G2} \cdot Y^{2}} + {{G3} \cdot Y^{3}} + {{G4} \cdot Y^{4}} + \ldots}\quad \right) \cdot Z^{2}} +} \\{{\left( {{H0} + {{H1} \cdot Y} + {{H2} \cdot Y^{2}} + {{H3} \cdot Y^{3}} + {{H4} \cdot Y^{4}} + \ldots}\quad \right) \cdot Z^{3}} +} \\{{\left( {{I0} + {{I1} \cdot Y} + {{I2} \cdot Y^{2}} + {{I3} \cdot Y^{3}} + {{I4} \cdot Y^{4}} + \ldots}\quad \right) \cdot Z^{4}} +} \\{{\left( {{J0} + {{J1} \cdot Y} + {{J2} \cdot Y^{2}} + {{J3} \cdot Y^{3}} + {{J4} \cdot Y^{4}} + \ldots}\quad \right) \cdot Z^{5}} +} \\{\ldots + \ldots}\end{matrix}$Herein, Y denotes the main scanning direction, Z denotes the subscanning direction, Cm or 1/Rm denotes the paraxial curvature in themain scanning direction around the optical axis, Cs(0) or 1/Rs(0)denotes the paraxial curvature in the sub scanning direction around theoptical axis, Cs(Y) denotes the paraxial curvature in the sub scanningdirection at a position Y in the main scanning direction, Kz(Y) denotesthe conical constant representing the secondary curvature surface in thesub scanning direction at the position Y in the main scanning direction,and f_(SAG)(Y,Z) denotes the high-order aspheric compensation value,wherein:Cs=1/Rs0+B1·Y+B2·Y ² +B3·Y ³ +B4·Y ⁴ +B5·Y ⁵+Kz=C0+C1·Y+C2·Y ² +C3·Y ³ +C4·Y ⁴ +C5·Y ⁵+

Note that when a value other than 0 is substituted for the coefficientsB1, B3, B5 . . . , which are the coefficients for Y to the power ofuneven numbers, the curvature radius in the sub scanning direction willbe asymmetrical to the main scanning direction.

Similarly, when a value other than 0 is substituted for the coefficientsC1, C3, C5 . . . , F1, F3, F5 . . . , G1, G3, G5 which are thecoefficients for Y to the power of uneven numbers representing thenon-curvature values, the non-curvature values in the sub scanningdirection will be asymmetrical to the main scanning direction.

(Embodiment 1)

In the following, the change in the beam pitch in the optical scanningdevice shown in FIG. 1 obtained from the above formulas describing thesurface configurations are given.

‘Light Source’

-   14 μm-pitch 4-channel LDA-   wavelength: 780 nm-   slanting angle: 12.39°

‘Coupling Lens’

-   focal length: 27 mm-   coupling effect: collimating effect

‘Polygon Mirror’

-   number of reflective surfaces: 5-   in-circle radius: 18 mm-   Angle formed between the incident angle of the beam emitted from the    light source and the optical axis of the scanning optical system:    60°-   Write width: ±150 mm-   Field angle: ±38°-   Write density: 1200 dpi-   d1=3 mm, d2=9.2 mm, d3=3 mm, d4=8.15 mm, d5=6 mm, d6=114 mm,    Curvature radius of the surface of incidence 10 a of the resin lens    10: −119.97 mm (spherical);-   Curvature radius of the exit surface 10 b of the resin lens 10: ∞    (main scanning) and 16.4 mm (sub scanning);-   Curvature radius of the surface of incidence 11 a of the resin lens    11: ∞ (main scanning) and −16 mm (sub scanning);-   Curvature radius of the exit surface 11 b of the resin lens 11: ∞    (main scanning) and 18.03 mm (sub scanning);-   Curvature radius of the surface of incidence 12 a of the glass    toroidal lens 12: 1.0E+08 (main scanning) and 13.54 mm (sub scanning    non-curvature surface)-   Curvature radius of the exit surface 12 b of the glass toroidal lens    12: −186 mm (spherical).-   Configuration of the surface of incidence 12 a of the glass toroidal    lens 12:

Rm = 1.00 + 08, Rs = 13.54, A04 −1.167576−07, A06   1.236756−11, C00−8.413895−01, C02 −7.014231−04, C04   7.664337−05, C06   7.406181−06,C08 −8.915899−08, I00 −5.984409−05, I02 −9.295456−08, I04 −1.267730−08,I06   1.645283−10, I08 −5.745329−12, K00   1.108638−07, K02  1.241363−08, K04 −9.523815−11, K08   6.477626−11,Reflective index of the resin lenses 10 and 11: 1.523978 (when λ=780 nm,temperature=25° C.);

-   Line expansion coefficient of the resin lenses 10 and 11: 7×10 ⁻⁵;-   Refractive index of the glass toroidal lens 12: 1.733278 (when λ=780    nm, temperature=25° C.);-   Line expansion coefficient of the glass toroidal lens: 5.4×10 ⁻⁶;-   Line expansion coefficient of the lens mounting member (base    member): 2.3×10⁻⁵;-   d7=71.6 mm, d8=30 mm, d9=66.3 mm, d10=8.5 mm, d11=159.3 mm, d12=0.2    mm, d13=0.2 mm,-   Refractive index of the resin scanning lenses 61 and 62: 1.523978    (when λ=780 nm, temperature=25° C.)-   Line expansion coefficient of the resin scanning lenses 61 and 62:    7×10 ⁻⁵;-   Configuration of the surface of incidence 61 a of the resin scanning    lens 61:

Rm = −1030.233346, Rs = −89.518927, A00 −4.041619E+02, A04  6.005017E−08, A06 −7.538155E−13, A08 −4.036824E−16, A10  4.592164E−20, A12 −2.396524E−24, B01 −9.317851E−06, B02  3.269905E−06, B03   4.132497E−09, B04 −4.207716E−10, B05−1.170114E−12, B06   4.370640E−14, B07   2.347965E−16, B08−6.212795E−18, B09 −3.967994E−20, B10 −3.873869E−21, B11   3.816823E−24,B12   4.535843E−25,

-   Configuration of the exit surface 61 b of the resin scanning lens    61:

Rm = −109.082474, Rs = −110.881332, A00 −5.427642E−01, A04  9.539024E−08, A06   4.882194E−13, A08 −1.198993E−16, A10  5.029989E−20, A12 −5.654269E−24, B02 −3.652575E−07, B04  2.336762E−11, B06   8.426224E−14, B08 −1.026127E−17, B10−2.202344E−21, B12   1.224555E−26,

-   Configuration of the surface of incidence 62 a of the resin scanning    lens 62:

Rm = 1493.654587, Rs = −70.072432, A00   5.479389E+01, A04−7.606757E−09, A06 −6.311203E−13, A08   6.133813E−17, A10 −1.482144E−21,A12   2.429275E−26, A14 −1.688771E−30, B02 −8.701573E−08, B04  2.829315E−11, B06 −1.930030E−15, B08   2.766862E−20, B10  2.176995E−24, B12 −6.107799E−29,

-   Configuration of the exit surface 62 b of the resin scanning lens 62    (sub scanning non-curvature surface):

Rm = 1748.583900, Rs = −28.034612, A00 −5.488740E+02, A04 −4.978348E−08,A06   2.325104E−12, A08 −7.619465E−17, A10   3.322730E−21, A12−3.571328E−26, A14 −2.198782E−30, B01 −1.440188E−06, B02   4.696142E−07,B03   1.853999E−11, B04 −4.153092E−11, B05 −8.494278E−16, B06  2.193172E−15, B07   9.003631E−19, B08 −9.271637E−21, B09−1.328111E−22, B10 −1.409647E−24, B11   5.520183E−27, B12  4.513104E−30, C00 −9.999999E−01, I00 −1.320849E−07, I02 −1.087674E−11,I04 −9.022577E−16, I06 −7.344134E−20, K00   9.396622E−09, K02  1.148840E−12, K04   8.063518E−17, K06 −1.473844E−20,

FIG. 4 shows a relationship between the image height and the scanningline position in the optical scanning device shown in FIG. 2B based onthe results obtained in embodiment 1. In this drawing, the scanning linepositions of channels 1 through 4 at temperatures of 25° C. and 45° C.are shown. At 25° C., the beam pitch between the channels is 21.2 μm,and at 45° C., the beam pitch is 20.7 μm. That is, the change in thebeam pitch is kept under control to a mere 0.5 μm.

FIGS. 5A and 5B are diagrams showing an optical scanning apparatusaccording to another embodiment of the present invention, wherein FIG.5A shows a schematic view of the optical scanning device, and FIG. 5Bshows a side view (optical path) of the same optical scanning device. Abundle of rays emitted from the light source 1 that has a plurality ofemission points are coupled into diverging rays by the coupling lens 2of the first optical system. The coupling lens 2 has a coaxialaspherical surface and the wave aberration of the bundle of rays emittedfrom the coupling lens 2 is suitably compensated for. The bundle of raysemitted from the coupling lens pass through an aperture stop 20 toobtain a desired beam spot diameter on the surface to be scanned 7,then, this is incident on a resin lens 13 of the second optical system3. A surface of incidence 13 a of the resin lens 13 has negative powersthat differ for each of the main scanning direction and the sub scanningdirection. More specifically, the resin lens 13 is an anamorphic lensthat has greater power in the sub scanning direction. Next, the bundleof rays emitted from the resin lens 13 is incident on a glass toroidallens 14 of the second optical system 3. Herein, the rays becomesubstantially parallel in the main scanning direction and are incidenton the light deflector 5. Also, in the sub scanning direction, thebundle of rays is condensed substantially into a line extending alongthe main scanning direction on the deflection surface of the deflector.The glass toroidal lens 14 may have a spherical surface and acylindrical surface. The third optical system 60 that includes the resinscanning lenses 61 and 62 compensates for the field curvature in themain scanning direction and the sub scanning direction and opticalcharacteristics such as fθ and focuses the bundle of rays deflected bythe light deflector 5 onto the surface to be scanned 7. In the presentexample, the resin lenses 61 and 62 have functions of imaging parallelrays in the main scanning direction.

Also, prior to exposure of the valid write width, a synchronousdetection is performed. The write process starts after a fixed period oftime from the completion of the synchronous detection. At this point,the write process starting positions of the plurality of beams need tobe synchronized. Therefore, the bundle of rays is preferably condensedon the synchronous detection element at least in the main scanningdirection.

Herein, the changes in field curvature due to temperature change of theresin imaging elements (resin scanning lenses) 61 and 62 in the thirdoptical system 60 are compensated for by the negative powers of theresin lens 13 of the second optical system 3. Specifically, the changein field curvature in the main scanning direction is compensated for bythe power in the main scanning direction of the surface of incidence 13a of the resin lens 13, and the change in field curvature in the subscanning direction is compensated for by the power in the sub scanningdirection of the surface of incidence 13 a and the power of the exitsurface 13 b of the resin lens 13.

Because the power in the sub scanning direction is dispersed onto twosurfaces, the curvature radius can be increased compared to anembodiment in which the power in the sub scanning direction is dispersedonly on one surface. Note that in the drawing, 13 a, 14 a, 61 a, and 62a represent the planes of incidence of the resin lens 13, the glasstoroidal lens 14, and the resin scanning lenses 61 and 62, respectively,and 13 b, 14 b, 61 b, and 62 b represent the exit surfaces of the resinlens 13, the glass toroidal lens 14, and the resin scanning lenses 61and 62, respectively.

FIGS. 6A and 6B are diagrams for illustrating an optical scanning deviceaccording to another embodiment of the present invention in which thepower in the sub scanning direction is dispersed onto three surfaces.FIG. 6A shows a schematic view of the optical scanning device, and FIG.6B shows a side view (optical path) of the same optical scanning device.According to this embodiment, the power in the sub scanning direction ofthe second optical system 3 is dispersed onto three surfaces; thereby,the curvature radius can be enhanced even further. In this opticalscanning device, the bundle of rays that has passed through the firstoptical system made up of the coupling lens 2 is converted intodiverging rays by the resin lens 10 that has a power in the mainscanning direction. A positive refractive power is provided in the mainscanning direction of the second optical system 3 made up of the resinlens 10 having a power in the main scanning direction, the resin lens 11having a power in the sub scanning direction, and the glass toroidallens 12 so that the bundle of rays in the main scanning directionpassing through the second optical system can be converted fromdiverging rays to substantially parallel rays. As a result, the focuspoint of the bundle of rays (the imaging point of the substantiallyparallel rays) and the intersecting point of the principal rays (theintersecting point of the parallel rays) will meet at substantially thesame point. Thereby, the dot displacements in the main scanningdirection can be prevented when the surface to be scanned is adjusted tothe focus point.

Also, the image height at the beginning of the write process and theimage height at the end of the write process are substantially the sameeven when the angles at the deflection surface of the deflector (in thisexample, the reflection angles of the light deflector 5) are different.Thus, it is possible to maintain consistency in the write width (thescanning width) of the beams, and unevenness in image density, anddistortion of vertical lines can be prevented.

As mentioned above, the resin lens 10 has a power in the main scanningdirection. Thus, by moving the resin lens 10 in the optical axisdirection, the misplacement of a beam waist in the main scanningdirection caused by a processing error of the third optical system 60and the like can be adjusted and fixed to be positioned substantially onthe surface to be scanned 7.

Also, the resin lens 11 and the glass toroidal lens 12 have powers inthe sub scanning direction. Thus, by moving the resin lens 11 in theoptical axis direction, the misplacement of the beam waist in the subscanning direction caused by a processing error of the third opticalsystem 60 and the like can be adjusted and fixed to be positionedsubstantially on the surface to be scanned 7.

The resin lens 10 may have different negative powers in the mainscanning direction and in the sub scanning direction. In this case, evenwhen the beam waist is misplaced in the sub scanning direction by movingthe resin lens 10 in the optical axis direction and adjusting themisplacement of the beam waist in the main scanning direction to bepositioned substantially on the surface to be scanned 7, the resin lens11 can be used to adjust and fix this misplacement of the beam waist inthe sub scanning direction to be substantially positioned on the surfaceto be scanned 7 since the resin lens 11 has a power only in the subscanning direction. Note that in the drawing, 10 a, 11 a, 12 a, 61 a,and 62 a represent the planes of incidence of the resin lens 10, 11, theglass toroidal lens 12, and the resin scanning lenses 61 and 62,respectively, and 10 b, 11 b, 12 b, 61 b, and 62 b represent the exitsurfaces of the resin lens 10, 11, the glass toroidal lens 12, and theresin scanning lenses 61 and 62, respectively.

In the following, further improvements (1 through 3) that can be made bycoupling the bundle of rays passing through the first optical systeminto diverging rays rather than coupling them into parallel rays as inthe first embodiment (FIGS. 2A, 2B, and FIG. 3) will be described withreference to FIGS. 7A, 7B, 8A, and 8B.

FIGS. 7A and 7B show examples of a bundle of rays emitted from anemission point that pass through the first optical system and the secondoptical system. FIG. 7A shows the bundle of rays in the optical scanningapparatus that converts the rays passing through the first opticalsystem into parallel rays, and FIG. 7B shows the bundle of rays in theoptical scanning apparatus that converts the rays passing through thefirst optical system into diverging rays.

1. To obtain equivalent beam spot diameters in the two different opticalscanning devices, a measurement ω shown in FIGS. 7A and 7B needs to befixed. In this case, the effective diameter of the coupling lens 2(effective diameter of the rays) Δ2 in the embodiment in which the raysemitted from a semiconductor laser array having a plurality of emissionpoints and passing through the coupling lens are converted intodiverging rays is smaller compared with the effective ray diameter Δ1 inthe embodiment in which the rays are converted into parallel rays. Thus,by making the outer diameter of the lens smaller, the size and cost ofthe optical scanning device can be reduced, and by having a smalleffective diameter of the rays, the wave aberration can be suitablyadjusted and the optical performance can be improved.

FIGS. 8A and 8B show examples of light ray bundles between the emissionpoint and the aperture stop. FIG. 8A shows the bundle of rays in theoptical scanning device that converts the rays passing through the firstoptical system into parallel rays, and FIG. 8B shows the bundle of raysin the optical scanning device that converts the rays passing throughthe first optical system into diverging rays.

2. Normally, a bundle of rays, emitted from a semiconductor laser arrayhaving a plurality of emission points and passed through the couplinglens, is converted into parallel rays. However, in such a case, ghostlight reflected from the aperture stop 21 is condensed and directed backto the emission point 1 as shown in FIG. 7A; thereby possibly creatinginstability in the intensity of the emitted light. The instability inlight intensity can cause unevenness in the image density. Thus, byconverting the rays passing through the coupling lens 2 into divergingrays, as shown in FIG. 8B, the ghost light reflected by the aperturestop 21 can be prevented from being condensed and directed back to theemission point. Also, a stable light intensity can be obtained, therebypreventing the generation of unevenness in image density.

3. In the optical scanning device that converts a bundle of rays intodiverging rays, the magnification in the sub scanning direction can belowered, and the degradation of the beam spacing in the sub scanningdirection on the surface to be scanned 7 as a result of a change in theemission point position (emission point spacing) caused by such factorsas the mounting of the light source device or a change in temperaturecan be reduced.

On the other hand, the spacing of the scanning line on the surface to bescanned needs to be set to a value according to the pixel density. Giventhat Pls denotes the emission point spacing in the sub scanningdirection, Ps denotes the scanning line spacing on the surface to bescanned, and β denotes the lateral magnification in the sub scanningdirection between the light source and the surface to be scanned, thescanning line spacing Ps can be set in accordance with the followingformula:

 Ps=Pls×β

Thus, to set the scanning line spacing to a value that corresponds to ahigh pixel density, (21.2 μm in the case of 1200 dpi), either thelateral magnification in the sub scanning direction between the lightsource and the surface to be scanned (β) needs to be reduced or theemission point spacing in the sub scanning direction (Pls) needs to bereduced. However, if the lateral magnification in the sub scanningdirection between the light source and the surface to be scanned (β) isreduced, the aperture diameter in the sub scanning direction will alsobe reduced, thereby lowering the light usage efficiency so thatsufficient light will not reach the surface to be scanned. On the otherhand, the reduction of the emission point spacing in the sub scanningdirection (Pls) is generally limited to a dozen or so μm in order toavoid influences from thermal cross talk and the like. Thus, it ispreferable that the plurality of emission points be arranged so that theline of emission points are inclined with respect to the sub scanningdirection within a plane that is perpendicular to the optical axis.

By using the optical scanning device with an inclined semiconductorlaser array, the scanning line spacing can be set to a valuecorresponding to a high density (for example, the spacing can be set to21.2 μm for a density of 1200 dpi).

Further, by providing a positive refractive power in the main scanningdirection of the second optical system so that the bundle of rayspassing through the second optical system is converted intosubstantially parallel rays in the main scanning direction, the focalpoint (the imaging point of the substantially parallel rays) and theintersecting point of the principal rays (the intersecting point of theparallel rays) meet at substantially the same point. Thus, when thesurface to be scanned is adjusted to the focus spot, the displacement ofdots in the main scanning direction can also be accurately controlled.Further, the image height at the start of the write process and theimage height at the end of the write process are the same height evenwhen the angles at the deflection surface of the deflector (e.g. thereflection angles of the polygon mirror) are different. Therefore, thewrite width of each of the beams (scanning width) can be arranged to beconsistent, and unevenness in density and distortion of the verticallines can be avoided.

FIG. 9 is a cross-sectional view in the sub scanning direction of theoptical scanning device according to the present invention showing thelens power distribution and aperture positions. In the drawing, theaperture stop 21 is arranged between the first optical system and thesecond optical system. Given that L1 denotes the distance from anoptical element of the first optical system that is arranged closest tothe second optical system to the aperture stop 21, and L2 denotes thedistance from the aperture stop 21 to an optical element of the secondoptical system that is arranged closest to the light source, when L1<L2,the distance between a conjugate point of the aperture stop 21 in thesub scanning direction and the surface to be scanned 7 becomes longer.In the drawing, an aperture stop 21 a is arranged within a range thatsatisfies the condition L1<L2, and an aperture stop 21 b is arrangedwithin a range that satisfies the condition L1>L2.

The aperture stop 21 functions as an entrance pupil of the opticalsystem starting from its position and onward. Thus, the plurality ofbeams advance toward the surface to be scanned, at different angles fromthe conjugate point. When the conjugate point is close to the surface tobe scanned, as in a conjugate point 21 b′ of the aperture stop 21 b, theplurality of beams advancing toward the surface to be scanned, will haverelatively large angles, and the scanning line spacing will differ foreach image height depending on the field curvature in the sub scanningdirection. Also, when the conjugate point is close to the surface to bescanned 7, the depth of the beam spot diameter in the sub scanningdirection will be greatly influenced by diffraction, and thereby lessflexibility will be allowed.

On the other hand, when the conjugate point is arranged to satisfy thecondition L1<L2 as in the conjugate point 21 a′ of the aperture stop 21,the distance between the conjugate point 21 a′ of the aperture stop 21 aand the surface to be scanned 7 will be greater compared to that betweenthe conjugate point 21 b′ of the aperture stop 21 b and the surface tobe scanned 7, and the scanning line spacing corresponding to each of theimage heights formed by a plurality of beams become consistent. Also,the influence from diffraction can be reduced, thereby allowing moreflexibility in the depth of the beam spot diameter in the sub scanningdirection.

FIG. 10 is a diagram of a laser printer as an example of an imagingapparatus that implements the scanning device of the present invention.The laser printer 100 in this drawing has a latent image holder 111,which is a light conductive photoconductor formed into a cylindricalshape. In the vicinity of the latent image holder 111, a charge roller112, which is charging means, a developing device 113, a transfer roller114, and a cleaning device 115 are implemented. A corona charger may beused as the charging device. Also, an optical scanning device 117 thatscans an image using laser beams (LB) so as to realize ‘exposure byoptical writing’ between the charge roller 112 and the developing device113 is implemented. Further, the laser printer 100 includes a fixingdevice 116, a cassette 118, a pair of resist rollers 119, a paper feedroller 120, a carrier path 121, a pair of delivery rollers 122, a tray123, and transfer paper P as the recording medium.

In an imaging process of the laser printer 100, the latent image holder111 rotates clockwise at a constant pace, and its surface is evenlycharged by the charge roller 112. This surface is then exposed by theoptical writing of the laser beams (LB) from the optical scanning device117 and an electrostatic latent image is formed thereon. Thiselectrostatic latent image is the so-called ‘negative latent image’ andits image portion is exposed. Then, the developing device 113 performsreversal development on this electrostatic latent image and a tonerimage is formed on the latent image holder 111.

The cassette 118 holding the transfer paper P is detachably arranged tothe laser printer body 100. When this cassette 118 is fixed to the laserprinter body 100 as in the drawing, the uppermost sheet of transferpaper P in the cassette 118 is fed to the paper feed roller 120. Thenthe pair of resist rollers 119 catches the leading tip of this transferpaper P entering the laser printer 100. The pair of resist rollers 119sends this transfer paper P into a transfer unit at a suitable timing inaccordance with the time at which the toner image on the latent imageholder 111 is moved to a transfer position. The transfer paper P and thetoner image meet at the transfer unit, and an electrostatic transfer ofthe toner image is realized by means of the transfer roller 114. Thetransfer paper P with the toner image transferred thereon is sent to thefixing device 116, wherein the toner image is fixed. Then, the transferpaper P passes through the carrier path 121 and is delivered onto thetray 123 by means of the pair of delivery rollers 122.

The surface of the latent image holder 111 is cleaned at the cleaningdevice 115 after the completion of the transferring of the toner imageso that undesirable substances such as residual toner particles andpaper dust are removed.

The imaging apparatus 100 that forms a latent image on a latent imageholder 111 through optical scanning and acquires a desired recordedimage by making the above latent image visible implements the scanningdevice according to the present invention for performing the opticalscanning on the latent image holder 111. More specifically, the latentimage holder 111 is a light conductive photoconductor on whichelectricity is evenly charged and optical scanning is performed to forman electrostatic latent image, this electrostatic latent image beingmade visible as a toner image.

(Embodiment 2)

In the following, the change in the beam spot diameter in the opticalscanning device shown in FIGS. 5A and 5B obtained from the aboveformulas describing the surface configurations are given.

‘Light Source’

-   14 μm-pitch 4-channel LDA-   wavelength: 780 nm-   inclination angle: 50.68°

‘Coupling Lens’

-   focal length: 27 mm-   coupling effect: diverging effect

‘Polygon Mirror’

-   number of reflective surfaces: 5-   in-circle radius: 18 mm-   Angle formed between the incident angle of the beam emitted from the    light source and the optical axis of the scanning optical system:    60°-   Write width: ±150 mm-   Field angle: ±38°-   Write density: 1200 dpi-   L1=8 mm, L2=39.4 mm, d1=3 mm, d2=20.35 mm, d3=6 mm, d4=138.5 mm,-   Curvature radius of the surface of incidence 13 a of the resin lens    13: −135.34 mm (main scanning) and −30 mm (sub scanning);-   Curvature radius of the exit surface 13 b of the resin lens 13: ∞    (main scanning) and 20 mm (sub scanning);-   Curvature radius of the surface of incidence 14 a of the glass    toroidal lens 14: ∞ (main scanning) and 27.561 mm (sub scanning);-   Curvature radius of the exit surface 14 b of the glass toroidal lens    14: −200 mm (spherical surface);-   Refractive index of the resin lens 13: 1.523978 (when λ=780 nm, and    temperature=25° C.)-   Line expansion coefficient of the resin lens 13: 7×10³¹ ⁵,-   Refractive index of the glass toroidal lens 14: 1.733109 (when λ=780    nm, and temperature=25° C.)-   Line expansion coefficient of the glass toroidal lens 14: 5.4×10³¹    ⁶,-   Line expansion coefficient of the lens mounting part (base member):    2.31×10⁻⁵,-   d7=71.6 mm, d8=30 mm, d9=66.3 mm, d10=8.5 mm, d11=159.3 mm, d12=0.2    mm, d13=0.2 mm,-   Refractive index of the resin scanning lenses 61 and 62: 1.523978    (when λ=780 nm, and temperature=25° C.)-   Line expansion coefficient of the resin lenses 61 and 62: 7×10⁻⁵,-   Configuration of the surface of incidence 61 a of the resin scanning    lens 61:

Rm = −1030.233346, Rs = −89.518927, A00 −4.041619E+02, A04  6.005017E−08, A06 −7.538155E−13, A08 −4.036824E−16, A10  4.592164E−20, A12 −2.396524E−24 B01 −9.317851E−06, B02   3.269905E−06,B03   4.132497E−09, B04 −4.207716E−10, B05 −1.170114E−12, B06  4.370640E−14 B07   2.347965E−16 B08 −6.212795E−18 B09 −3.967994E−20B10 −3.873869E−21 B11   3.816823E−24 B12   4.535843E−25

-   Configuration of the surface of incidence 61 a of the resin scanning    lens 61 is as follows:

Rm = −1030.233346, Rs = −89.518927, A00 −4.041619E+02, A04  6.005017E−08, A06 −7.538155E−13, A08 −4.036824E−16, A10  4.592164E−20, A12 −2.396524E−24, B01 −9.317851E−06, B02  3.269905E−06, B03   4.132497E−09, B04 −4.207716E−10, B05−1.170114E−12, B06   4.370640E−14, B07   2.347965E−16, B08−6.212795E−18, B09 −3.967994E−20, B10 −3.873869E−21, B11   3.816823E−24,B12   4.535843E−25,

-   Configuration of the exit surface 61 b of the resin scanning lens    61:

Rm = −109.082474, Rs = −110.881332, A00 −5.427642E−01, A04  9.539024E−08, A06   4.882194E−13, A08 −1.198993E−16, A10  5.029989E−20, A12 −5.654269E−24, B02 −3.652575E−07, B04  2.336762E−11, B06   8.426224E−14, B08 −1.026127E−17, B10−2.202344E−21, B12   1.224555E−26,

-   Configuration of the surface of incidence 62 a of the resin scanning    lens 62:

Rm = 1493.654587, Rs = −70.072432, A00   5.479389E+01, A04−7.606757E−09, A06 −6.311203E−13, A08   6.133813E−17, A10 −1.482144E−21,A12   2.429275E−26, A14 −1.688771E−30, B02 −8.701573E−08, B04  2.829315E−11, B06 −1.930080E−15, B08   2.766862E−20, B10  2.176995E−24, B12 −6.107799E−29,

-   Configuration of the exit surface 61 b of the resin scanning lens 61    (sub scanning direction, non-curvature surface):

Rm = 1748.583900, Rs = −28.034612, A00 −5.488740E+02, A04 −4.978348E−08,A06   2.325104E−12, A08 −7.619465E−17, A10   3.322730E−21, A12−3.571328E−26, A14 −2.198782E−30, B01 −1.440188E−06, B02   4.696142E−07,B03   1.853999E−11, B04 −4.153092E−11, B05 −8.494278E−16, B06  2.193172E−15, B07   9.003631E−19, B08 −9.271637E−21, B09−1.328111E−22, B10 −1.409647E−24, B11   5.520183E−27, B12  4.513104E−30, C00 −9.999999E−01, I00 −1.320849E−07, I02 −1.087674E−11,I04 −9.022577E−16, I06 −7.344134E−20, K00   9.396622E−09, K02  1.148840E−12, K04   8.063518E−17, K06 −1.473844E−20,

(Embodiment 3)

In the following, the change in the beam spot diameter in the opticalscanning device shown in FIGS. 5A and 5B obtained from the aboveformulas describing the surface configurations are given.

‘Light Source’

-   14 μm-pitch 4-channel LDA-   wavelength: 780 m-   slanting angle: 10.457°

‘Coupling Lens’

-   focal length: 27 mm-   coupling effect: diverging effect

‘Polygon Mirror’

-   number of reflective surfaces: 5-   in-circle radius: 18 mm-   Angle formed between the incident angle of the beam emitted from the    light source and the optical axis of the scanning optical system:    60°-   Write width: ±150 mm-   Field angle: ±38°-   Write density: 1200 dpi-   L1=8 mm, L2=39.4 mm, d1=3 mm, d2=9.2 mm, d3=3 mm, d4=8.15 mm, d5=6    mm, d6=115.7 mm,-   Curvature radius of the surface of incidence 10 a of the resin lens    10: −119.97 mm (spherical);-   Curvature radius of the exit surface 10 b of the resin lens 10: ∞    (main scanning) and 16.4 mm (sub scanning);-   Curvature radius of the surface of incidence 11 a of the resin lens    11: ∞ (main scanning) and −16 mm (sub scanning);-   Curvature radius of the exit surface 11 b of the resin lens 11: ∞    (main scanning) and 18.03 mm (sub scanning);-   Curvature radius of the surface of incidence 12 a of the glass    toroidal lens 12: 1.0E+08 (main scanning) and 13.568 mm (sub    scanning direction, non-curvature surface)-   Curvature radius of the exit surface 12 b of the glass toroidal lens    12: −179.47 mm (spherical).    Configuration of the surface of incidence 12 a of the glass toroidal    lens 12:

Rm = 1.00 + 08, Rs = 13.568, A04 −1.167576−07, A06   1.236756−11, C00−8.413895−01, C02 −7.014231−04, C04   7.664337−05, C06   7.406181−06,C08 −8.915899−08, I00 −5.984409−05, I02 −9.295456−08, I04 −1.267730−08,I06   1.645283−10, I08 −5.745329−12, K00   1.108638−07, K02  1.241363−08, K04 −9.523815−11, K08   6.477626−11,

-   Reflective index of the resin lenses 10 and 11: 1.523978 (when λ32    780 nm, temperature=25° C.);-   Line expansion coefficient of the resin lenses 10 and 11: 7×10⁻⁵;-   Refractive index of the glass toroidal lens 12: 1.733109 (when λ=780    nm, temperature=25° C.);-   Line expansion coefficient of the glass toroidal lens 12: 5. 4×10⁻⁶.-   Line expansion coefficient of the lens mounting member (base    member): 2.31×10⁻⁵;-   d7=71.6 mm, d8=30 mm, d9=66.3 mm, d10=8.5 mm, d11=159.3 mm, d12=0.2    mm, d13=0.2 mm,-   Refractive index of the resin scanning lenses 61 and 62: 1.523978    (when λ=780 nm, temperature=25° C.)-   Line expansion coefficient of the resin scanning lenses 61 and 62:    7×10⁻⁵;-   Configuration of the surface of incidence 61 a of the resin scanning    lens 61:

Rm = −1030.233346, Rs = −89.518927, A00 −4.041619E+02, A04  6.005017E−08, A06 −7.538155E−13, A08 −4.036824E−16, A10  4.592164E−20, A12 −2.396524E−24, B01 −9.317851E−06, B02  3.269905E−06, B03   4.132497E−09, B04 −4.207716E−10, B05−1.170114E−12, B06   4.370640E−14, B07   2.347965E−16, B08−6.212795E−18, B09 −3.967994E−20, B10 −3.873869E−21, B11   3.816823E−24,B12   4.535843E−25,

-   Configuration of the exit surface 61 b of the resin scanning lens    61:

Rm = −109.082474, Rs = −110.881332, A00 −5.427642E−01, A04  9.539024E−08, A06   4.882194E−13, A08 −1.198993E−16, A10  5.029989E−20, A12 −5.654269E−24, B02 −3.652575E−07, B04  2.336762E−11, B06   8.426224E−14, B08 −1.026127E−17, B10−2.202344E−21, B12   1.224555E−26,

-   Configuration of the surface of incidence 62 a of the resin scanning    lens 62:

Rm = 1493.654587, Rs = −70.072432, A00   5.479389E+01, A04−7.606757E−09, A06 −6.311203E−13, A08   6.133813E−17, A10 −1.482144E−21,A12   2.429275E−26, A14 −1.688771E−30, B02 −8.701573E−08, B04  2.829315E−11, B06 −1.930080E−15, B08   2.766862E−20, B10  2.176995E−24, B12 −6.107799E−29,

-   Configuration of the exit surface 61 b of the resin scanning lens 61    (sub scanning direction, non-curvature surface):

Rm = 1748.583900, Rs = −28.034612, A00 −5.488740E+02, A04 −4.978348E−08,A06   2.325104E−12, A08 −7.619465E−17, A10   3.322730E−21, A12−3.571328E−26, A14 −2.198782E−30, B01 −1.440188E−06, B02   4.696142E−07,B03   1.853999E−11, B04 −4.153092E−11, B05 −8.494278E−16, B06  2.193172E−15, B07   9.003631E−19, B08 −9.271637E−21, B09−1.328111E−22, B10 −1.409647E−24, B11   5.520183E−27, B12  4.513104E−30, C00 −9.999999E−01, I00 −1.320849E−07, I02 −1.087674E−11,I04 −9.022577E−16, I06 −7.344134E−20, K00   9.396622E−09, K02  1.148840E−12, K04   8.063518E−17, K06 −1.473844E−20

Note that although not shown in the drawing, a soundproof glass with athickness of 1.9 mm (refractive index: 1.511) and a dustproof glass alsowith a thickness of 1.9 mm (refractive index: 1.511) are inserted in theoptical scanning device. The soundproof glass is mounted with aninclination of 8° within the deflection surface, and the dustproof glassis mounted with an inclination of 20° within the sub scanningcross-sectional surface. Also, the diverging angles of the laser diodearray (LDA) as half angles are θ⊥=30° and θ//=9°, and the aperture isarranged on the diverging rays at a position that satisfies thecondition L1<L2 so that the field depth of the beam spot can be within asufficiently wide range.

Summing up the results obtained in the above, by setting the aperturediameter to 6.4 (main scanning)×1.8 (sub scanning) in embodiment 2, astable beam spot diameter can be obtained for each image height asindicated in table 1 shown below.

TABLE 1 Image Height (mm) −150 0 150 Main Scanning 38 μm 37 μm 38 μm SubScanning 39 μm 39 μm 39 μm

Also, by setting the aperture diameter to 8 (main scanning)×1.6 (subscanning) in embodiment 3, a stable beam spot diameter can be obtainedfor each image height as indicated in table 2 shown below.

TABLE 2 Image Height (mm) −150 0 150 Main Scanning 29 μm 28 μm 29 μm SubScanning 28 μm 28 μm 28 μm

In the above description of the preferred embodiments, a semiconductorlaser array is used as the light source having a plurality of emissionpoints; however, the present invention is not limited to implementingthis particular type of light source and variations and modificationsare possible without departing from the scope of the present invention.For example, the light source having a plurality of emission points maybe created by the synthesis of rays using a prism and the like.

According to the present invention, even when a resin lens is used asthe scanning lens, a change in the beam pitch due to environmentaltemperature change can be controlled.

Also, by arranging the surface configuration of at least one of theresin imaging elements in the second optical system to effectivelycompensate for a field curvature change due to temperature change at asupport member of the first optical system and/or at the resin imagingelement of the third optical system, image degradation such asdisplacement of dots in the main scanning direction or unevenness inimage density and distortion of the vertical lines due to the differencein the write width (scanning width) of each beam can be reduced even ifthe bundle of rays passing through the coupling optical system isconverted into diverging rays and the magnification in the sub scanningdirection is lowered. Further, compared to the conventional art in whichthe misplacement of the imaging position is compensated for and themisplacement of the imaging position is mechanically adjusted, thepresent invention enables cost reduction as well as a reduction of powerconsumption. By reducing the size of the outer diameter of the lens, thesize of the optical scanning device can be reduced and thereby costs canalso be reduced. Also, since the effective diameter is reduced, waveaberration can be compensated for and the optical characteristics can beimproved. Further, when an aperture stop is arranged between the firstoptical system and the light deflector, ghost light reflected by thedeflector is prevented from being condensed and directed back to theemission point. Thus, a stable light intensity can be obtained and thegeneration of unevenness in density can be prevented.

The present application is based on and claims the benefit of theearlier filing date of Japanese priority application No.2002-129741filed on May 1, 2002, the entire contents of which are herebyincorporated by reference.

1. A multi-beam optical scanning device, comprising: a light sourcehaving a plurality of emission points that emit a bundle of rays; afirst optical system that couples the bundle of rays emitted from thelight source; a second optical system that condenses the bundle of raysfrom the first optical system into a substantially linear stateextending along a main scanning direction; a light deflector that has adeflection surface arranged close to where the bundle of rays iscondensed, wherein the bundle of rays is deflected by said deflectionsurface; a third optical system that condenses the deflected bundle ofrays onto a surface to be scanned as a plurality of light spots; whereinthe third optical system has at least one resin imaging element; thesecond optical system has at least one resin imaging element and atleast one glass imaging element; and a power of each surface of theresin imaging element of the second optical system is arranged so that achange in a beam pitch in a sub scanning direction caused by atemperature change in at least one of the first optical system and thethird optical system satisfies a condition:ΔP′<0.5/DPI (mm/° C.) wherein ΔP′ denotes a measure of change in the subscanning beam pitch on an image surface for every 1° C. temperaturechange (mm/° C.), and DPI denotes a write density (dots/inch).
 2. Animaging apparatus comprising a multi-beam optical scanning device thatincludes: a light source having a plurality of emission points that emita bundle of rays; a first optical system that couples the bundle of raysemitted from the light source; a second optical system that condensesthe bundle of rays from the first optical system into a substantiallylinear state extending along a main scanning direction; a lightdeflector that has a deflection surface arranged close to where thebundle of rays is condensed, wherein the bundle of rays is deflected bysaid deflection surface; a third optical system that condenses thedeflected bundle of rays onto a surface to be scanned as a plurality oflight spots; wherein the third optical system has at least one resinimaging element; the second optical system has at least one resinimaging element and at least one glass imaging element; and a power ofeach surface of the resin imaging element of the second optical systemis arranged so that a change in beam pitch in a sub scanning directioncaused by a temperature change in at least one of the first opticalsystem and the third optical system satisfies a condition:ΔP′<0.5/DPI (mm/° C.) wherein ΔP′ denotes a measure of change in the subscanning beam pitch on an image surface for every 1° C. temperaturechange (mm/° C.), and DPI denotes a write density (dots/inch).